Revisiting the top-quark pair production at future $e^{+}{e}^{-}$ colliders

Abstract

In this paper, we reanalyze the top-quark pair production at the next-to-next-to-leading order (NNLO) in QCD at future $e^{+}{e}^{-}$ colliders by using the Principle of Maximum Conformality (PMC) method. The PMC renormalization scales in ${\alpha }_s$ are determined by absorbing the non-conformal $\beta$ terms by recursively using the Renormalization Group Equation (RGE). Unlike the conventional scale-setting method of fixing the scale at the center-of-mass energy ${\mu }_r=\sqrt{s}$, the determined PMC scale $Q_{\star }$ is far smaller than the $\sqrt{s}$ and increases with the $\sqrt{s}$, yielding the correct physical behavior for the top-quark pair production process. Moreover, the convergence of the pQCD series for the top-quark pair production is greatly improved due to the elimination of the renormalon divergence. For a typical collision energy of $\sqrt{s}=500$ GeV, the PMC scale is $Q_{\star }=107$ GeV; the QCD correction factor $K$ for conventional results is $K\sim 1+0.1244_{-0.0087-0.0011}^{+0.0102+0.0012}+0.0184_{+0.0061-0.0003}^{-0.0086+0.0002}$, where the first error is caused by varying the scale ${\mu }_r\in [\sqrt{s}/2,2\sqrt{s}]$ and the second error is from the top-quark mass $\Delta m_t=\pm 0.7$ GeV. After applying the PMC, the renormalization scale uncertainty is eliminated and the QCD correction factor $K$ is improved to $K\sim 1+0.1507_{-0.0015}^{+0.0015}-0.0057_{-0.0000}^{+0.0001}$, where the error is from the top-quark mass $\Delta m_t=\pm 0.7$ GeV. The PMC improved predictions for the top-quark pair production are helpful for detailed studies of properties of the top-quark at future $e^{+}{e}^{-}$ colliders.

Comments: 8 pages, 3 figures. Accepted by Chinese Physics C